{
  "id": "1805.11116",
  "version": "v1",
  "published": "2018-05-28T18:06:51.000Z",
  "updated": "2018-05-28T18:06:51.000Z",
  "title": "The Chern-Schwartz-MacPherson class of an embeddable scheme",
  "authors": [
    "Paolo Aluffi"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "There is an explicit formula expressing the Chern-Schwartz-MacPherson class of a hypersurface in a nonsingular variety (in characteristic $0$) in terms of the Segre class of its jacobian subscheme; this has been known for a number of years. We generalize this formula to arbitrary embeddable schemes: for every subscheme $X$ of a nonsingular variety $V$, we define an associated subscheme $Y$ of a projective bundle over $V$ and provide an explicit formula for the Chern-Schwartz-MacPherson class of $X$ in terms of the Segre class of $Y$. If $X$ is a local complete intersection, a version of the result yields a direct expression for the Milnor class of $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-28T18:06:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chern-schwartz-macpherson class",
      "explicit formula",
      "nonsingular variety",
      "segre class",
      "local complete intersection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}